The Syriacs (Orthodox and Catholic), Chaldean Catholics, Church of the East (COE), and Maronites are most likely the same people from the beginning. However, in early Christianity the Syriacs (and those Syriacs who became Maronites) were on the Roman side of the border while the COE were on the Persian side (in the Roman-Persian war) so since then we have been split.
The Chaldean Catholics and Church of the East are definitely the same. The Chaldean name was just applied to distinguish the Nestorians who converted to Catholicism from those who stayed Nestorian (but today some Chaldeans are trying to make it as if they're from the ancient Chaldeans).
We're either Assyrian or Aramean ethnically. In the Syriac churches the Aramean name is majority (there's a good amount of Assyrian proponents as well though), in the Church of the East Assyrian is naturally a huge majority (they changed their church name to Assyrian Church of the East in the 20th century), the Chaldean Catholics also have a good amount of Assyrian proponents but many of them call themselves Chaldean, the Maronite church is being approached mostly by the Aramean proponents who are trying to get them on their side (some Maronites consider themselves to be from the ancient Phoenicians though). Some Melkites were probably also Syriacs from the start.
It's really the Greeks fault that we're in this mess today. If it wasn't for them the word Syria and Syrian probably wouldn't exist. They encountered Assyria with and without the initial vowel aleph (which is like the latin a) when they first came into contact with the Near East regions and rendered them as Assyria (Assuria, Assurios, etc.) and Syria (Suria, Surios, etc.) in Greek (so the word Syria is derived from Assyria) and at first they used the words interchangeably (in the beginning they pretty much called all people in Mesopotamia, Syrians/Assyrians, even if you were Aramean or something else). But with time each word got more specific meanings...
A couple of examples:
Justinus, 3rd century AD: "His successors too, following his example, gave answers to their people through their ministers. The Assyrians, who were afterwards called Syrians, held their empire thirteen hundred years. The last king that reigned over them was Sardanapalus, a man more effeminate than a woman."
Posidonius, 1st century BC: "The people we [Greeks] call Syrians were called by the Syrians themselves Arameans." (the Aramean proponents say that the word Syrian was taken up by us because of Greek influence at around the 4th century AD, before that we only used Aramean to designate ourselves)
It's people throwing quotes at each other to try to get people to their own movement (the Assyrian nationalist movement is older than the Aramean one though).
Don't confuse the above Syria/Syrian with today's Syrian Arab Republic and it's population. Most Syriac Orthodox are from what today is Southeast Turkey originally. When most people read Syrian Orthodox they probably think: "Oh, Orthodox Christians from Syria", but that is wrong (that's why we changed it to Syriac, to not be confused with Syria and it's Arab population).